The general solution of the equation $\sec 4\theta -\sec 2\theta =2\text{ is }\theta =$

$\frac{1}{\cos 4\theta }-\frac{1}{\cos 2\theta }=2$

$\begin{array}{l}\Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\cos 2\theta -\cos 4\theta =2\cos 4\theta \cos 2\theta =\cos 6\theta +\cos 2\theta \\ \therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\cos 6\theta +\cos 4\theta =0\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\cos 5\theta \cos \theta =0\\ \cos \theta =0\Rightarrow \theta =(2n+1)\frac{\pi }{2},\cos 5\theta =0\Rightarrow \theta =(2n+1)\frac{\pi }{10}\end{array}$